dependent variable of function

The variable x is called the independent variable of function f and variable y is called the dependent variable of function f. We clear the concept of dependent and independent variable of function by figure

dependent variable of function


For now onward, we shall only consider the function in which the variables are real numbers, and we say that f is a real value function of real number

Real valued function example


We have the function f(x) = x³-2x²+4x-1

(i)  f(0) = ?

f (x) = x³-2x²+4x-1

f(0)=0-0+0-1= -1

(ii) f(1) =?

f (x) = x³-2x²+4x-1

f(1) = 1-2+4-1 = +2

(iii) f(-2) = ?

f (x) = x³-2x²+4x-1

f(-2)= (-2)³-2(-2)²+4(-2)-1

=   – 8- 8-8-1= -25

(iv) f(1+x) =?

f (x) = x³-2x²+4x-1

f(1+x)= (1+x)³-2(1+x)²+4(1+x)-1

f(1+x) = x³+x²+3x+2

(v) f(1/x) =? Where x ≠ 0

f (x) = x³-2x²+4x-1


=   1/x³-2/x²+4/x-1 Where x ≠ 0

Function notation:

if a variable y depends on a variable x in such a way that

each value of x determine exactly one value of y, then we say that

“y is a function of x” 

Swiss mathematician Euler(1707-1783) invented a symbolic way to

write the statement “y is a function of x” 

as y=f(x) which read as” y is equal to x”

Explanation of function:

A function can be considered as a computing machine f that takes an input x,

exactly one output f(x). This output f(x) is called the value of f at x or image of x under f.

The output f(x) is denoted by a single letter, say y, we write y= f(x)

Definition of function, domain, range 

A function f from a set X to a set Y is a rule or a correspondence that assigns

to each element x in X a unique element y in Y. the set X is called the Domain of f.

The set of corresponding element y in Y is called the Range of f.